Results 1 to 2 of 2

Math Help - Matrix Representation of Linear Transformations

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    14

    Matrix Representation of Linear Transformations

    Let V be an n-dimensional vector space with an ordered basis B.
    Define T: V F^n by T(x) = [x]B. Prove that T is linear.



    Note that the [x]B is suppose to be a subscript B
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by Qt3e_M3 View Post
    Let V be an n-dimensional vector space with an ordered basis B.
    Define T: V F^n by T(x) = [x]B. Prove that T is linear.



    Note that the [x]B is suppose to be a subscript B
    You just need to show: (i) T(k\bold{v}) = kT(\bold{v}) i.e. [k\bold{v}]_B = k[\bold{v}]_B (ii) T(\bold{v}+\bold{w}) = T(\bold{v}) + T(\bold{w}) i.e. [\bold{v}+\bold{w}]_B = [\bold{v}]_B + [\bold{w}]_B.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Matrix Representation of Linear Transformation
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 1st 2011, 08:38 PM
  2. matrix representation of the linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 11th 2011, 05:30 PM
  3. Matrix Representation of Linear Transformations (2)
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 4th 2008, 09:59 PM
  4. matrix representation of linear algebra
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: June 30th 2008, 04:55 PM
  5. Replies: 0
    Last Post: February 2nd 2008, 08:24 PM

Search Tags


/mathhelpforum @mathhelpforum